Tangliu Wen

Tangliu Wen

Proving linearizability of concurrent data structures is crucial for ensuring their correctness, but is challenging especially for implementations that employ sophisticated synchronization techniques. In this paper, we propose a new proof technique for verifying linearizability of concurrent stacks. We first prove the soundness of the elimination mechanism, a common optimization used in concurrent stacks, which enables simplifying the linearizability proofs. We then present a stack theorem that reduces the problem of proving linearizability to establishing a set of conditions based on the happened-before order of operations. The key idea is to use an extended partial order to capture when a pop operation can observe the effect of a push operation. We apply our proof technique to verify two concurrent stack algorithms: the Treiber stack and the Time-Stamped stack, demonstrating its practicality. Our approach provides a systematic and compositional way to prove linearizability of concurrent stacks.

Tangliu Wen

Linearizability is a commonly accepted consistency condition for concurrent objects. Filipović et al. show that linearizability is equivalent to observational refinement. However, linearizability does not permit concurrent objects to share memory spaces with their client programs. We show that linearizability (or observational refinement) can be broken even though a client program of an object accesses the shared memory spaces without interference from the methods of the object. In this paper, we present strict linearizability which lifts this limitation and can ensure client-side traces and final-states equivalence even in a relaxed program model allowing clients to directly access the states of concurrent objects. We also investigate several important properties of strict linearizability. At a high level of abstraction, a concurrent object can be viewed as a concurrent implementation of an abstract data type (ADT). We also present a correctness criterion for relating an ADT and its concurrent implementation, which is the combination of linearizability and data abstraction and can ensure observational equivalence. We also investigate its relationship with strict linearizability.